Crystalline Structures
CHAPTER 3: CRYSTAL
STRUCTURES & PROPERTIES
ISSUES TO ADDRESS...
• How do atoms assemble into solid structures?
(for now, focus on metals)
• How does the density of a material depend on its structure?
• When do material properties vary with the sample (i.e., part) orientation?
Chapter 3- 1
ENERGY AND PACKING
• Non dense, random packing
Energy typical neighbor bond length
typical neighbor bond energy
• Dense, regular packing
r
Energy typical neighbor bond length
typical neighbor bond energy
r
Dense, regular-packed structures tend to have lower energy.
Chapter 3- 2
MATERIALS AND PACKING
Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of: -metals
-many ceramics
-some polymers
crystalline SiO2
Adapted from Fig. 3.22(a),
Callister 7e.
Si
Oxygen
Noncrystalline materials...
• atoms have no periodic packing
• occurs for: -complex structures
-rapid cooling
"Amorphous" = Noncrystalline
noncrystalline SiO2
Adapted from Fig. 3.22(b),
Callister 7e.
Chapter 3- 3
METALLIC CRYSTALS
• tend to be densely packed.
• have several reasons for dense packing:
-Typically, only one element is present, so all atomic radii are the same.
-Metallic bonding is not directional.
-Nearest neighbor distances tend to be small in order to lower bond energy.
• have the simplest crystal structures.
We will look at three such structures...
Chapter 3- 4
Chapter 3-
α=β==90o
Cubic
a=b=c
Hexagonal
a=b≠c α=β=90o,=120o
Tetragonal
a=b≠c
Rhombohedral a=b=c
α=β==90o α=β=≠ 90o
Orthorrhombic a≠b≠c α=β==90o
Monoclinic
Triclinic
a≠b≠c α==90o,β ≠ 90o a≠b≠c α≠β≠≠90o
Chapter 3-
SIMPLE CUBIC STRUCTURE (SC)
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)
Chapter 3- 5
ATOMIC PACKING FACTOR
APF =
Volume of atoms in
STRUCTURES & PROPERTIES
ISSUES TO ADDRESS...
• How do atoms assemble into solid structures?
(for now, focus on metals)
• How does the density of a material depend on its structure?
• When do material properties vary with the sample (i.e., part) orientation?
Chapter 3- 1
ENERGY AND PACKING
• Non dense, random packing
Energy typical neighbor bond length
typical neighbor bond energy
• Dense, regular packing
r
Energy typical neighbor bond length
typical neighbor bond energy
r
Dense, regular-packed structures tend to have lower energy.
Chapter 3- 2
MATERIALS AND PACKING
Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of: -metals
-many ceramics
-some polymers
crystalline SiO2
Adapted from Fig. 3.22(a),
Callister 7e.
Si
Oxygen
Noncrystalline materials...
• atoms have no periodic packing
• occurs for: -complex structures
-rapid cooling
"Amorphous" = Noncrystalline
noncrystalline SiO2
Adapted from Fig. 3.22(b),
Callister 7e.
Chapter 3- 3
METALLIC CRYSTALS
• tend to be densely packed.
• have several reasons for dense packing:
-Typically, only one element is present, so all atomic radii are the same.
-Metallic bonding is not directional.
-Nearest neighbor distances tend to be small in order to lower bond energy.
• have the simplest crystal structures.
We will look at three such structures...
Chapter 3- 4
Chapter 3-
α=β==90o
Cubic
a=b=c
Hexagonal
a=b≠c α=β=90o,=120o
Tetragonal
a=b≠c
Rhombohedral a=b=c
α=β==90o α=β=≠ 90o
Orthorrhombic a≠b≠c α=β==90o
Monoclinic
Triclinic
a≠b≠c α==90o,β ≠ 90o a≠b≠c α≠β≠≠90o
Chapter 3-
SIMPLE CUBIC STRUCTURE (SC)
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)
Chapter 3- 5
ATOMIC PACKING FACTOR
APF =
Volume of atoms in